Variations on Sacharov's problem

[wrobel]

Here is an interesting problem (in my opinion at least)

A rubber band is placed on a horizontal table and attached to a vertical wall by its left end. A disk of given mass and radius is placed on the band without initial velocity. Then the right end of the band is being drawn with constant speed $v$. Find the motion of the disk.
It turns out that the kinetic energy of the disk vanishes as $t\to \infty$ while the disk rolls away in the right direction to infinity .
The disk does not slip. Very simple but nonholonomic problem by the way.


Original Sacharov's problem: a bug creeps to the right along the band with a speed $u$ wrt the band. Will the bug catch up a hand which draws the end of the band?

Hope I remember it correctly.

 

[martinbn]

https://www.feynmanlectures.caltech.edu/info/exercises/bug_on_band.html

 

[wrobel]

Nice resource but the problem
https://www.feynmanlectures.caltech.edu/info/exercises/rough_inclined_plane.html
is spoiled:) Good question would be: At what values of the parameters does the trajectory have an asymptote?

 

[martinbn]

Nice resource but the problem
https://www.feynmanlectures.caltech.edu/info/exercises/rough_inclined_plane.html
is spoiled:) Good question would be: At what values of the parameters does the trajectory have an asymptote?

I gave it for the historical part. Feyman says that he gave the problem to Sakharov.

 

[wrobel]

Feyman says that he gave the problem to Sakharov.

Feynman also said that he invented the differentiation of an improper integral to calculate it. He must have worked under the pseudonym Euler in the 18th century as well.

 

[martinbn]

Feynman also said that he invented the differentiation of an improper integral to calculate it. He must have worked under the pseudonym Euler in the 18th century as well.

Did he actually say that?

 

[wrobel]

Did he actually say that?

I must apologize, I have just looked through "Surely You're Joking, Mr. Feynman" In this text he definitely says that he learnt this technique from a textbook of analysis.
It seems I was guided by this
google